Earlier quoted context omitted.
The deeper you go, the higher the pressure. The higher the pressure, the smaller the (trapped) air bubbles. The smaller the air bubbles, the lower the upward force. As a result, the deeper you go, the more air you will need to pump into your tank. Or in other words: with a given amount of air inside your tank, there's a maximum depth you can go. If you go deeper, the air bubbles will no longer lift the tank.
Of course, and that's what happened to Kursk. But: The released air would go up, regardless how pressured it is. While going up it would decompress taking up more space and therefore having greater force to push the tank up (as I mentioned, released air would be capture in a construction similar to a tree with leaves. Imagine leaves upside-down capturing the air. I'm sure you can find different type of mix that would…
It's the basic law of conservation of energy. You need to provide the energy required to lift the tank by compressing the air. The energy required to lift the tank is mgh (mass of tank, gravitational constant, height to lift the tank). The energy stored inside the tank is proportional to p*V (pressure times volume). You can't lift the tank further than the amount of energy you have available, so you can never have a surplus of energy.